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Non-root users should not be able to modify the history/versions of a file: Fits. Git is just used as backend, and mounted as file system. So only normal file system operations should be possible unless the user has direct write access to the repo – which you can prevent easily.

supports Linux: Yes.

open source: Yes.

Additional hints: if the underlying repo is owned by root and resides on the local machine, tig is a great text-mode client to browse the history by anyone having at least read access to the repo. If you want to host it on a different machine, Gitea is a very easy way to do that (I use it on a BananaPi; it's very light on resources).